factor x^2 - 30*x + 2817 in sqrt(-2)
Is there a way I can use SAGE to factor my polynomial x^2 - 30*x + 2817 in sqrt(-2).
2 Answers
I think you are looking for the roots of the polynomial:
f = x^2 - 30*x + 2817
f.roots()
which gives:
[(-36*I*sqrt(2) + 15, 1), (36*I*sqrt(2) + 15, 1)]
This would mean that your original function is equal to:
$$ x^2-30x+2817 = \left(x-(15-36 \sqrt{-2})\right)\left(x-(15+36\sqrt{-2})\right)$$
Comments
Note that you can also work over the field QQbar of algebraic numbers.
Here is how you would factor your polynomial there and find its roots.
sage: P.<x> = QQbar[]
sage: p = x^2 - 30*x + 2817
sage: p.factor()
(x - 15.00000000000000? - 50.91168824543143?*I) * (x - 15.00000000000000? + 50.91168824543143?*I)
sage: p.roots()
[(15.00000000000000? - 50.91168824543143?*I, 1),
(15.00000000000000? + 50.91168824543143?*I, 1)]
If you want a radical expression for the roots:
sage: for r in p.roots():
....: print(r[0].radical_expression())
....:
-36*I*sqrt(2) + 15
36*I*sqrt(2) + 15
Comments
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Asked: 2016-11-02 06:47:32 +0200
Seen: 390 times
Last updated: Nov 03 '16
Note that we write Sage rather than SAGE.